Number System
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Q.

What is the remainder left after dividing $1!+2!+3!.....+100!$ by $7$?

 A.

0

 B.

5

 C.

14

 D.

21

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Solution:
Option(B) is correct

$7!+8!+9!.......+100!$ is completely divisible by $7$.

Now, $1!+2!+3!....+6! = 873$

When $873$ is divided by $7$ it leaves a remainder $= \textbf{5}.$


(2) Comment(s)


Poonam Pipaliya
 ()

sir how can you say that 7!+8!+.....+100! is completely divided by 7...??..!!please elaborate it.


Parag
 ()

u can take 7! common.

7x6x5x4x3x2x1( 8+9x8+ 10x9x8 + and so on....) will always be divisible by 7.